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The time-dependent magnetohydrodynamic flow past a flat plate

Published online by Cambridge University Press:  28 March 2006

G. F. Carrier
Affiliation:
Pierce Hall, Harvard University
H. P. Greenspan
Affiliation:
Pierce Hall, Harvard University

Abstract

Two time-dependent magnetohydrodynamic flow problems are discussed. In Part I we consider the situation in which a semi-infinite flat plate is moved impulsively in its own plane into an electrically conducting viscous fluid. The ambient magnetic field has the same direction as the motion of the plate; it is found that when $\mu H^2_0| \rho U^2_0 \; \textless \; 1$, the flow pattern approaches asymptotically the steady flow found earlier (Greenspan & Carrier 1959). When $\mu H^2_0| \rho U^2_0 \; \textgreater \; 1$, the asymptotic state is one in which the fluid accompanies the plate in a rigid body motion as was anticipated in the earlier work.

In Part II, an infinite plate is moved impulsively in its own plane in the presence of an ambient magnetic field which is perpendicular to the plane of the plate. It is shown that the problem is not uniquely set until one specifies what three-dimensional problem reduces in the limit to the two-dimensional problem so defined. The answers in the conceptually acceptable limit case investigated here (the plate being a pipe of very large radius) have an asymmetry which at first sight is unexpected.

Type
Research Article
Copyright
© 1960 Cambridge University Press

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References

Carrier, G. F. 1959 A useful approximation procedure for Wiener-Hopf problems. J. Appl. Phys. (in the Press).Google Scholar
Carrier, G. F. & Lewis, J. A. 1949 Some remarks on the flat plate boundary layer. Quart. Appl. Math. 7, 228.Google Scholar
Greenspan, H. P. & Carrier, G. F. 1959 The magneto-hydrodynamic flow past a flat plate. J. Fluid Mech. 6, 77.Google Scholar
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